View the Spectrogram Using Spectrum Analyzer

Spectrograms are a two-dimensional representation of the power spectrum of a signal as
this signal sweeps through time. They give a visual understanding of the frequency
content of your signal. Each line of the spectrogram is one periodogram computed using
either the filter bank approach or the Welch’s algorithm of averaging modified
periodogram.

To show the concepts of the spectrogram, this example uses the model
ex_psd_sa as the starting point. Note that Simulink® models are not supported in MATLAB
Online.

Open the model and double-click the Spectrum Analyzer block. In the
Spectrum Settings pane, change View to
Spectrogram. The Method is set to
Filter bank. Run the model. You can see the spectrogram
output in the spectrum analyzer window. To acquire and store the data for further
processing, create a Spectrum Analyzer Configuration object and
run the getSpectrumData function on this object.

Colormap

Power spectrum is computed as a function of frequency f and is
plotted as a horizontal line. Each point on this line is given a specific color
based on the value of the power at that particular frequency. The color is chosen
based on the colormap seen at the top of the display. To change the colormap, click View > Configuration Properties, and choose one of the options in color
map. Make sure View is set to
Spectrogram. By default, color
map is set to jet(256).

The two frequencies of the sine wave are distinctly visible at 5 kHz and 10 kHz.
Since the spectrum analyzer uses the filter bank approach, there is no spectral
leakage at the peaks. The sine wave is embedded in Gaussian noise, which has a
variance of 0.0001. This value corresponds to a power of -40 dBm. The color that
maps to -40 dBm is assigned to the noise spectrum. The power of the sine wave is
26.9 dBm at 5 kHz and 10 kHz. The color used in the display at these two frequencies
corresponds to 26.9 dBm on the colormap. For more information on how the power is
computed in dBm, see 'Conversion of power in watts to dBW and dBm'.

To confirm the dBm values, change View to
Spectrum. This view shows the power of the signal at
various frequencies.

You can see that the two peaks in the power display have an
amplitude of about 26 dBm and the white noise is averaging around -40 dBm.

Display

In the spectrogram display, time scrolls from top to bottom, so the most recent data is shown at the top of the
display. As the simulation time increases, the offset time also increases to keep the vertical axis limits
constant while accounting for the incoming data. The Offset value, along with the simulation
time, is displayed at the bottom-right corner of the spectrogram scope.

Resolution Bandwidth (RBW)

Resolution Bandwidth (RBW) is the minimum frequency bandwidth that can be resolved
by the spectrum analyzer. By default, RBW (Hz) is set to
Auto. In the auto mode, RBW is
the ratio of the frequency span to 1024. In a two-sided spectrum, this value is Fs/1024, while in a one-sided spectrum, it is (Fs/2)/1024. In this example, RBW is (44100/2)/1024 or 21.53 Hz.

If the Method is set to Filter
bank, using this value of RBW, the number of
input samples used to compute one spectral update is given by Nsamples =
Fs/RBW, which is 44100/21.53 or 2048 in this example.

If the Method is set to Welch,
using this value of RBW, the window length
(Nsamples) is computed iteratively using this
relationship:

Nsamples=(1−Op100)×NENBW×FsRBW

Op is the amount of overlap between
the previous and current buffered data segments. NENBW is the
equivalent noise bandwidth of the window.

For more information on the details of the spectral estimation algorithm, see
Spectral Analysis.

To distinguish between two frequencies in the display, the distance between the
two frequencies must be at least RBW. In this example, the distance between the two
peaks is 5000 Hz, which is greater than RBW. Hence, you
can see the peaks distinctly.

Change the frequency of the second sine wave from 10000 Hz to 5015 Hz. The
difference between the two frequencies is 15 Hz, which is less than
RBW.

On zooming, you can see that the peaks are not distinguishable.

To increase the frequency resolution, decrease RBW to 1 Hz
and run the simulation. On zooming, the two peaks, which are 15 Hz apart, are now
distinguishable

Time Resolution

Time resolution is the distance between two spectral lines in the vertical axis.
By default, Time res (s) is set to
Auto. In this mode, the value of time resolution is
1/RBW s, which is the minimum attainable resolution. When you
increase the frequency resolution, the time resolution decreases. To maintain a good
balance between the frequency resolution and time resolution, change the
RBW (Hz) to Auto. You can also
specify the Time res (s) as a numeric value.

Convert the Power Between Units

The spectrum analyzer provides three units to specify the power spectral density:
Watts/Hz, dBm/Hz, and
dBW/Hz. Corresponding units of power are
Watts, dBm, and
dBW. For electrical engineering applications, you can also
view the RMS of your signal in Vrms or
dBV. The default spectrum type is Power
in dBm.

Convert the Power in Watts to dBW and dBm

Power in dBW is given by:

PdBW=10log10(powerinwatt/1watt)

Power in dBm is given by:

PdBm=10log10(powerinwatt/1milliwatt)

For a sine wave signal with an amplitude of 1 V, the power of
a one-sided spectrum in Watts is given
by:

PWatts=A2/2PWatts=1/2

In this example, this
power equals 0.5 W. Corresponding power in dBm is given by:

For a white noise signal, the spectrum is flat for all frequencies.
The spectrum analyzer in this example shows a one-sided spectrum in
the range [0 Fs/2]. For a white noise signal with a variance of 1e-4,
the power per unit bandwidth (Punitbandwidth)
is 1e-4. The total power of white noise in watts over
the entire frequency range is given by:

The number of frequency
bins is the ratio of total bandwidth to RBW. For a one-sided spectrum,
the total bandwidth is half the sampling rate. RBW in this example
is 21.53 Hz. With these values, the total power of white noise in watts is 0.1024 W. In dBm, the power of white
noise can be calculated using 10*log10(0.1024/10^-3),
which equals 20.103 dBm.

Convert Power in Watts to dBFS

If you set the spectral units to dBFS and set the full scale (FullScaleSource) to
Auto, power in dBFS is computed as:

PdBFS=20⋅log10(Pwatts/Full_Scale)

where:

Pwatts is the power in watts

For double and float signals, Full_Scale is the maximum value of the input signal.

For fixed point or integer signals, Full_Scale is the maximum value that can be
represented.

If you specify a manual full scale (set FullScaleSource to
Property), power in dBFS is given by:

PFS=20⋅log10(Pwatts/FS)

Where FS is the full scaling factor specified in the FullScale property.

For a sine wave signal with an amplitude of 1 V, the power of a one-sided spectrum in
Watts is given by:

PWatts=A2/2PWatts=1/2

In this example, this power equals 0.5 W and the maximum input signal for a sine wave is 1 V. The
corresponding power in dBFS is given by:

PFS=20⋅log10(1/2/1)

Here, the power equals -3.0103. To confirm this value in the spectrum analyzer, run these commands:

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